We continue with a discussion of the condition (REF ) above. This can be understood as a tail condition: For any compact set \(K\subseteq (0,\infty )^3\)  we have by Lemma REF  that \(f_{\varphi _{I,n},\varphi _{G,n}}\)  converges uniformly to \(f_{\varphi _I,\varphi _G}\) . Thus, if we restrict the integral in the definition of \(C_{\alpha }(f_{\varphi _I,\varphi _G},f_{\varphi _{I,n},\varphi _{G,n}})\)  to \(K\) , the restricted integral remains bounded. Note also that by choosing \(\alpha >0\)  small, possible singularities of \(f_2\)  are integrable. Hence, (REF ) is only restrictive for the integral over \(K^c\) . Thus, if \(f_{\varphi _I,\varphi _G}\)  is compactly supported (REF ) follows. Note furthermore that \(f_{\varphi _I,\varphi _G}\)  is compactly supported if \(\varphi _I, \varphi _G\)  and \(\varphi _W\)  are compactly supported. In our specific epidemics setting for COVID-19, this is a highly plausible assumption because people stop being infectious at some point. However, for other diseases people can stay infectious for an extended period of time, e.g. for Hepatitis C, the mean generation time is about 20 years (cf. [1]}).
